I invite anyone with a proper knowledge of cocktails to fill any gaps I left or correct any partial names that I got wrong in the lists in panel 1. Some I think are made up (I'm pretty sure "Double Spoiler" isn't a cocktail, unless it was named after the Touhou game), but I don't think that accounts for all the ones I couldn't find.

The difference is that if you just ask for a Rum and Coke you might not get the lime wedge (unless you ask for it).

She looks more like she's holding in a massive dump than laughter.